Method of determining two-stage codebook set applicable to 4tx cross-polarized antenna configuration

ABSTRACT

The invention provides a solution of designing a two-stage codebook set applicable to 4Tx cross-polarized antenna configuration and a method of determining a codebook in a multi-input multi-output communication system based upon the designed two-stage codebook set applicable to 4Tx cross-polarized antenna configuration. The first stage codebook relates long-term/wideband channel information and is based on DFT vectors, whereas the second stage codebook relates to short-term/narrowband channel information and is base on selecting columns of the first stage codebook and providing inter-polarization phase information.

FIELD OF THE INVENTION

The present disclosure relates to wireless communications andparticularly to a method of designing a two-stage codebook setapplicable to 4Tx cross-polarized antenna configuration in a Multi-InputMulti-Output (MIMO) wireless communication system and a method ofdetermining a codebook from the two-stage codebook set.

BACKGROUND OF THE INVENTION

A Multi-User Multi-Input Multi-Output (MU-MIMO) system can achieve afull multiplexing gain and a significant throughput improvement is bymeans of linear beamforming precoding at a transmitter. The accuracy ofchannel information acquisition has a significant influence on the gainof the MU-MIMO system in Frequency Division Duplex (FDD) configuration.

For the MU-MIMO system, codebook feedback is a technology to realizechannel information acquisition and user scheduling. However codebookdesign adaptability and its granularity have become great challenges andbottlenecks in the MU-MIMO application in the FDD system. For example, acurrent Re1.10 4Tx codebook is not suitable for 4Tx cross-polarizedantenna configuration, which restricts an efficient application ofMU-MIMO.

SUMMARY OF THE INVENTION

In view of the foregoing problem, the invention proposes a solution ofdesigning a two-stage codebook set applicable to cross-polarized antennaconfiguration. The two-stage codebook set designed by the invention isapplicable to a multi-input multi-output communication system in which abase station is configured with four cross-polarized transmit antennas,and a method of generating a two-stage codebook set according to anembodiment of the invention includes the steps of:

-   -   a. generating a codebook matrix V based upon a two-antenna        rank-1 DFT codebook c;    -   b. determining the first-stage codebook set W, according to the        codebook matrix V, wherein

${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$

and

-   -   c. determining the two-stage codebook set W₂ at least based upon        a column selection vector and inter-polarization phase        information.

Advantageously the step a includes:

-   -   selecting two orthogonal DFT vectors from the two-antenna rank-1        DFT codebook c to generate the codebook matrix V, wherein

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\; \pi \; n}{N}}\end{bmatrix}}^{T}},{\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)\mspace{14mu} {and}}$${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\; \pi}{N}m} & ^{j\frac{2\; \pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right).}$

Advantageously the step a includes:

-   -   selecting two orthogonal DFT vectors from the two-antenna rank-1        DFT codebook c to generate a codebook matrix I, wherein

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$and ${I = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,{{\ldots \mspace{14mu} \frac{N}{2}} - 1}} \right);}$

and

-   -   left-multiplying or right-multiplying the codebook matrix I by a        diagonal matrix J to generate the codebook matrix V, wherein

${J = \begin{pmatrix}\rho & 0 \\0 & \sqrt{1 - \rho^{2}}\end{pmatrix}},$

and ρ is quantized in the range (0, 1).

Advantageously the step a includes:

-   -   selecting a set of adjacent overlapping DFT vectors from the        two-antenna rank-1 DFT codebook c to generate the codebook        matrix V, wherein

${V = \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix}},{\left( {{m = 0},2,4,\ldots \mspace{14mu},{N - 2}} \right).}$

Advantageously the step c includes:

-   -   determining the two-stage codebook set W₂ based upon the column        selection vector and the inter-polarization phase information in        the formula of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} \\{Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{3} \\{Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- Y_{4}}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 2×1 selection vector        in which all other elements than an n-th element being 1 are 0,        é₁ represents a first column selected from the codebook matrix        V, and {tilde over (e)}₂ represents a second column selected        from the codebook matrix V.

Advantageously the step c includes:

-   -   determining the second set W₂ based upon the column selection        vector, the inter-polarization phase information and        inter-polarization amplitude information in the formula of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n\; = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 2×1 selection vector        in which all other elements than an n-th element being 1 are 0,        {tilde over (e)}₁ represents a first column selected from the        codebook matrix V, {tilde over (e)}₂ represents a second column        selected from the codebook matrix V, and α is quantized in the        range (0, 1).

Advantageously the step c includes:

-   -   determining the second set W₂ based upon the column selection        vector, the inter-polarization phase information and        inter-polarization amplitude information in the formula of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}_(m), {tilde over (e)}_(k))}, (m=1, . . . 4,k=1, . . . , 4) for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, (i=1, . . . 4, j=1, . . . , 4,k=1, . . . 4, l=1, . . . , 4) for rank 2,

-   -   wherein é_(n) represents a 4×1 selection vector in which all        other elements than an n-th element being 1 are 0, {tilde over        (e)}₁ represents a first column selected from the codebook        matrix V, {tilde over (e)}₂ represents a second column selected        from the codebook matrix V, {tilde over (e)}₃, represents a        third column selected from the codebook matrix V, {tilde over        (e)}₄ represents a fourth column selected from the codebook        matrix V, and α is quantized in the range (0, 1).

Based upon a two-stage codebook set, designed by the invention,applicable to 4Tx cross-polarized antenna configuration, in anembodiment of the invention, there is provided a method of determining acodebook in a base station of a multi-input multi-output communicationsystem, wherein the method includes the steps of:

-   -   i. determining an uplink long-term and/or broadband channel        matrix according to a sounding signal from a user equipment;    -   ii. selecting a first codebook from a first-stage codebook set        based upon the first-stage codebook set to match the uplink        long-term and/or broadband channel matrix;    -   iii. sending index information of the first codebook to the user        equipment;    -   iv. receiving index information of a second codebook from the        user equipment;    -   v. selecting the second codebook from a second-stage codebook        set according to the index information of the second codebook;        and    -   vi. multiplying the first codebook with the second codebook to        obtain a target codebook,    -   wherein the first-stage codebook set W, and the second-stage        codebook set W₂ are determined by:        -   generating a codebook matrix V based upon a two-antenna            rank-1 DFT codebook c;        -   determining the first-stage codebook set W₁ according to the            codebook matrix V, wherein

${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$

-   -    and        -   determining the second-stage codebook set W₂ at least based            upon a column selection vector and inter-polarization phase            information.

Advantageously the codebook matrix V is generated by any one of:

-   -   selecting two orthogonal DFT vectors from the two-antenna rank-1        DFT codebook c to generate the codebook matrix V, wherein

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$and ${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right);}$

-   -   selecting two orthogonal DFT vectors from the two-antenna rank-1        DFT codebook c to generate a codebook matrix I, wherein

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$and ${I = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},\left( {{m = 0},1,{{\ldots \mspace{14mu} \frac{N}{2}} - 1}} \right),$

and left-multiplying or right-multiplying the codebook matrix I by adiagonal matrix J to generate the codebook matrix V, wherein

${J = \begin{pmatrix}\rho & 0 \\0 & \sqrt{1 - \rho^{2}}\end{pmatrix}},$

and ρ is quantized in the range (0, 1); and

-   -   selecting a set of adjacent overlapping DFT vectors from the is        two-antenna rank-1 DFT codebook c to generate the codebook        matrix V, wherein

${V = \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix}},{\left( {{m = 0},2,4,\ldots \mspace{14mu},{N - 2}} \right).}$

Advantageously the second-stage codebook set W, is determined by any oneof:

-   -   determining the second set W, based upon the column selection        vector and the inter-polarization phase information in the        formula of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 2×1 selection vector        in which all other elements than an n-th element being 1 are 0,        {tilde over (e)}₁ represents a first column selected from the        codebook matrix V, and {tilde over (e)}₂ represents a second to        column selected from the codebook matrix V;        -   determining the second set W₂ based upon the column            selection vector, the inter-polarization phase information            and inter-polarization amplitude information in the formula            of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 2×1 selection vector        in which all other elements than an n-th element being 1 are 0,        {tilde over (e)}₁ represents a first column selected from the        codebook matrix V {tilde over (e)}₂ represents a second column        selected from the codebook matrix V, and α is quantized in the        range (0, 1); and        -   determining the second set W₂ based upon the column            selection vector, the inter-polarization phase information            and inter-polarization amplitude information in the formula            of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}_(m), {tilde over (e)}_(k))}, (m=1, . . . 4,k=1, . . . , 4) for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, (i=1, . . . 4, j=1, . . . , 4,k=1, . . . 4, l=1, . . . , 4) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 4×1 selection vector        in which all other elements than an n-th element being 1 are 0,        {tilde over (e)}_(l) represents a first column selected from the        codebook matrix V, {tilde over (e)}₂ represents a second column        selected from the codebook matrix V, {tilde over (e)}₃        represents a third column selected from the codebook matrix V,        {tilde over (e)}₄ represents a fourth column is selected from        the codebook matrix V, and α is quantized in the range (0, 1).

In correspondence to the foregoing embodiment, in an embodiment of theinvention, there is provided a method of determining a codebook in auser equipment of a multi-input multi-output communication system,wherein the method includes the steps of:

-   -   A. receiving index information of a first codebook from a base        station;    -   B. selecting the first codebook from a first-stage codebook set        according to the index information of the first codebook;    -   C. determining a downlink short-term and/or narrowband channel        matrix according to reference information from the base station;    -   D. selecting a second codebook from a second-stage codebook set        based upon the first codebook to match the downlink short-term        and/or narrowband channel matrix; and    -   E. sending index information of the second codebook to the base        station and multiplying the first codebook with the second        codebook to obtain a target codebook,    -   wherein the first-stage codebook set W, and the second-stage        codebook set W₂ are determined by:        -   generating a codebook matrix V based upon a two-antenna            rank-1 DFT codebook c;        -   determining the first-stage codebook set W₁ according to the            codebook matrix V, wherein

${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$

-   -    and        -   determining the second-stage codebook set W₂ at least based            is upon a column selection vector and inter-polarization            phase information.

Advantageously the step D includes:

-   -   multiplying the first codebook with each codebook in the        second-stage codebook set and selecting the second codebook from        the second-stage codebook set based upon a maximum capacity or        minimum distance criterion.

Based upon a two-stage codebook set, designed by the invention,applicable to 4Tx cross-polarized antenna configuration, in anembodiment of the invention, there is provided a method of determining acodebook in a user equipment of a multi-input multi-output communicationsystem, wherein the method includes the steps of:

-   -   I. determining a downlink long-term and/or broadband channel        matrix according to reference information from a base station;    -   II. selecting a first codebook from a first-stage codebook set        to match the downlink long-term and/or broadband channel matrix;    -   III. sending index information of the first codebook to the base        station;    -   IV. determining a downlink short-term and/or narrowband channel        matrix according to the reference information from the base        station;    -   V. selecting a second codebook from a second-stage codebook set        based upon the first codebook to match the downlink short-term        and/or narrowband channel matrix; and    -   VI. sending index information of the second codebook to the base        station, and multiplying the first codebook with the second        codebook to obtain a target codebook,    -   wherein the first-stage codebook set W, and the second-stage        codebook set W₂ are determined by:        -   generating a codebook matrix V based upon a two-antenna            rank-1 DFT codebook c;        -   determining the first-stage codebook set W₁ according to the            codebook matrix V, wherein

${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$

-   -    and        -   determining the second-stage codebook set W₂ at least based            upon a column selection vector and inter-polarization phase            information.

Advantageously the codebook matrix V is generated by any one of:

-   -   selecting two orthogonal DFT vectors from the two-antenna rank-1        DFT codebook c to generate the codebook matrix V, wherein

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},\mspace{14mu} \left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$and ${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right);}$

-   -   selecting two orthogonal DFT vectors from the two-antenna rank-1        DFT codebook c to generate a codebook matrix I, wherein

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},\mspace{14mu} \left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$and ${I = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right),$

and left-multiplying or right-multiplying the codebook matrix I by adiagonal matrix J to generate the codebook matrix V, wherein

${J = \begin{pmatrix}\rho & 0 \\0 & \sqrt{1 - \rho^{2}}\end{pmatrix}},$

and ρ is quantized in the range (0, 1); and

-   -   selecting a set of adjacent overlapping DFT vectors from the        two-antenna rank-1 DFT codebook c to generate the codebook        matrix V, wherein

${V = \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix}},{\left( {{m = 0},2,4,\ldots \mspace{14mu},{N - 2}} \right).}$

Advantageously the second-stage codebook set W₂ is determined by any oneof:

-   -   determining the second set W₂ based upon the column selection        vector and the inter-polarization phase information in the        formula of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 2×1 selection vector        in which all other elements than an n-th element being 1 are 0,        {tilde over (e)}₁ represents a first column selected from the        codebook matrix V, and {tilde over (e)}₂ represents a second        column selected from the codebook matrix V;        -   determining the second set W₂ based upon the column            selection vector, the inter-polarization phase information            and inter-polarization amplitude information in the formula            of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 2×1 selection vector        in which all other elements than an n-th element being 1 are 0,        {tilde over (e)}₁ represents a first column selected from the        codebook matrix V, {tilde over (e)}₂ represents a second column        selected from the codebook matrix V, and α is quantized in the        range (0, 1); and        -   determining the second set W₂ based upon the column            selection vector, the inter-polarization phase information            and inter-polarization amplitude information in the formula            of:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂)ε{({tilde over (e)}_(m), {tilde over (e)}_(k))}, (m=1, . . . 4,k=1, . . . , 4) for rank 1; and

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, (i=1, . . . 4, j=1, . . . , 4,k=1, . . . 4, l=1, . . . , 4) for rank 2,

-   -   wherein {tilde over (e)}_(n) represents a 4 x 1 selection vector        in which all other elements than an n-th element being 1 are 0,        {tilde over (e)}₁ represents a first column selected from the        codebook matrix V, {tilde over (e)}₂ represents a second column        selected from the codebook matrix V, {tilde over (e)}₃        represents a third column selected from the codebook matrix V,        {tilde over (e)}₄ represents a fourth column selected from the        codebook matrix V, and α is quantized in the range (0, 1).

Advantageously the step V includes:

-   -   multiplying the first codebook with each codebook in the        second-stage codebook set and selecting the second codebook from        the second-stage codebook set based upon a maximum capacity or        minimum distance criterion.

In correspondence to the foregoing embodiment, in an embodiment of theinvention, there is provided a method of determining a codebook in abase station of a multi-input multi-output communication system, thebase station being configured with four cross-polarized transmitantennas, wherein the method includes the steps of:

-   -   receiving index information of a first codebook from a user        equipment;    -   selecting the first codebook from a first-stage codebook set        according to the index information of the first codebook;    -   receiving index information of a second codebook from the user        equipment;    -   selecting the second codebook from a second-stage codebook set        according to the index information of the second codebook; and    -   multiplying the first codebook with the second codebook to        obtain a target codebook,    -   wherein the first-stage codebook set W₁ and the second-stage        codebook set W₂ are determined by:    -   generating a codebook matrix V based upon a two-antenna rank-1        DFT codebook c;    -   determining the first-stage codebook set W₁ according to the        codebook matrix V, wherein

${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$

and

-   -   determining the second-stage codebook set W₂ at least based upon        a column selection vector and inter-polarization phase        information.

The respective aspects of the invention will become more apparent fromthe following description of particular embodiments.

BRIEF DESCRIPTION OF DRAWINGS

The foregoing and other features of the invention will become moreapparent upon review of the following detailed description ofnon-limiting embodiments taken with reference to the drawings in which:

FIG. 1 is a flow chart of a method of determining a codebook in amulti-input multi-output communication system according to an embodimentof the invention; and

FIG. 2 is a flow chart of a method of determining a codebook in amulti-input multi-output communication system according to anotherembodiment of the invention.

Identical or like reference numerals in the drawings denote identical orlike components.

DETAILED DESCRIPTION OF EMBODIMENTS

In the following we will give a detailed description of a two-stagecodebook structure applicable to 4Tx cross-polarized antennaconfiguration.

A two-stage codebook set can be defined as follows:

W=W ₁ W ₂

Where W₁ is a first-stage codebook set and W₂ is a second-stage codebookset.

(1) Generation of the First-Stage Codebook Set W₁

W₁ represents long-term and/or wideband channel properties for eachantenna pair with the same polarization direction in 4Tx cross-polarizedantenna configuration, as can be shown in the following block diagonalform:

$W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}$

V is composed of two eigenvectors for 2Tx MIMO channels with the samepolarization direction in 4Tx cross-polarized antenna configuration,that is, V=[v₁ v₂] with the dimension of 2×2.

There are two methods to acquire eigenvector information for the matrixV. One is downlink signaling indication and the other is uplink CSIfeedback.

In the first option, wideband eigenvectors, such as v₁ and v₂, and awideband eigenvalue ρ, can be achieved by a base station (eNB) accordingto the reciprocity of uplink and downlink covariance matrixes for eachantenna pair with the same polarization direction. Then the eNB notifiesa User Equipment (UE) of the calibrated eigenvectors and eigenvaluethrough downlink signaling to achieve completely the same W₁ informationfor the eNB side and the UE side. The eigenvectors and the eigenvalue inW₁ have a slow variation property based on the reciprocity of the uplinkand downlink covariance matrixes and can be semi-statically indicated bythe eNB through downlink signaling transmission in a long periodicity,which can occupy a downlink transmission overhead as low as possible.Thus in this option, a larger codebook set can be used to quantize thecovariance matrixes or their eigenvectors to improve W1 accuracy.

In the second option, V can be defined as a two-column orthogonal 2TxDFT codebook and can be selected and reported by the UE from apredefined codebook set.

For example, a two-antenna DFT codebook with rank 1 can be designed asfollows:

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

In an example, two orthogonal DFT vectors can be selected from theforegoing codebook c to form the following codebook matrix V:

${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right);}$

Thus W₁ can be shown as follows:

${W_{1} \in \left\{ \begin{bmatrix}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix} & 0 \\0 & \begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}\end{bmatrix} \right\}},\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right)$

Advantageously a non-constant modulus property can be taken into accountto reflect inter-polarization amplitude information, and hereupon theelement ρ reflecting the non-constant modulus property can be introducedto V. Specifically, firstly two orthogonal DFT vectors can be selectedfrom the foregoing codebook c to form the following codebook matrix I:

${I = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right)$

Then the foregoing codebook matrix I is left-multiplied orright-multiplied by a diagonal matrix

$J = \begin{pmatrix}\rho & 0 \\0 & \sqrt{1 - \rho^{2}}\end{pmatrix}$

to generate the codebook matrix V:

${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}\rho & \rho \\{\sqrt{1 - \rho}^{j\frac{2\pi}{N}m}} & {\sqrt{1 - \rho}^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}}\end{bmatrix}}},{{\left( {{m = 0},1,{{\ldots \mspace{14mu} \frac{N}{2}} - 1}} \right)\mspace{14mu} \left( {{Left}\mspace{14mu} {multiplication}} \right)};{and}}$${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}\rho & \rho \\{\sqrt{1 - \rho}^{j\frac{2\pi}{N}m}} & {\sqrt{1 - \rho}^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}}\end{bmatrix}}},{\left( {{m = 0},1,{{\ldots \mspace{14mu} \frac{N}{2}} - 1}} \right)\mspace{14mu} {\left( {{Right}\mspace{14mu} {multiplication}} \right).}}$

Where ρ is quantized in the range (0, 1).

In another example, a plurality of consecutive DFT vectors can beselected from the foregoing codebook c to form the codebook matrix V.For example, a set of adjacent overlapped DFT vectors can be selectedfrom the foregoing codebook c to form the codebook matrix V:

${V = \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix}},\left( {{m = 0},2,4,\ldots \mspace{14mu},{N - 2}} \right)$

Thus W₁ can be shown as follows:

${W_{1} \in \left\{ \begin{bmatrix}\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix} & 0 \\0 & \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix}\end{bmatrix} \right\}},\left( {{m = 0},2,4,\ldots \mspace{14mu},{N\text{?}\text{?}\text{indicates text missing or illegible when filed}}} \right.$

As can be appreciated, the size of the codebook set W₁ in the isforegoing first option can be set larger than the size of the codebookset W₁ in the foregoing second option.

Advantageously the eNB can signal semi-statically the selection of oneof the foregoing two options in higher-layer signaling. If the selectionof the first option is signaled in the higher-layer signaling, then theUE shall use W₁ directly according to downlink indication from the eNB;and if the selection of the second option is signaled in thehigher-layer signaling, then the UE measures a downlink channel andreports W₁ information over an uplink feedback channel. Otherwise, adefault selection of W₁ may be used, such as from the latest downlinkindication or uplink feedback.

In summary, the first-stage codebook set W₁ can be defined as follows:

For the foregoing first downlink signaling indication method:

$W_{1} = {\begin{bmatrix}V & 0 \\0 & V\end{bmatrix} = \begin{bmatrix}\left\lbrack {v_{1}\mspace{31mu} v_{2}} \right\rbrack & 0 \\0 & \left\lbrack {v_{1}\mspace{31mu} v_{2}} \right\rbrack\end{bmatrix}}$

For the foregoing second uplink CSI feedback method:

-   -   In the event that V is formed of two orthogonal DFT vectors        selected from the foregoing codebook c:

${W_{1} \in \left\{ \begin{bmatrix}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix} & 0 \\0 & \begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}\end{bmatrix} \right\}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right);}$

-   -   In the event that V is formed of a set of adjacent overlapped        DFT vectors selected from the foregoing codebook c:

${W_{1} \in \left\{ \begin{bmatrix}\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix} & 0 \\0 & \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix}\end{bmatrix} \right\}},\left( {{m = 0},2,4,\ldots \mspace{14mu},{\text{?}\text{?}\text{indicates text missing or illegible when filed}}} \right.$

The number of feedback bits for W₁ is

$\left\lceil {\log_{2}\left( \frac{N}{2} \right)} \right\rceil.$

The first-stage codebook set W₁ is the same for rank 1 and rank 2. Thesecond-stage codebook set W₂ is different for rank 1 and rank 2, and thesecond-stage codebook set W₂ can be obtained from the first-stagecodebook set W₁. How to obtain the second-stage codebook set W₂ will bedescribed below.

(2) Generation of the Second Stage Codebook Set W₂

W₂ represents short-term and/or subband channel properties of 4Txcross-polarized antenna. There are two elements which can be taken intoaccount for a W₂ design, such as column selection from the codebookmatrix V in W₁ and a co-phasing hypothesis.

The first element taken into account for a W₂ design is columnselection. A proper DFT vector is selected from the codebook matrix V inW₁. For example, a column selection vector Y can be defined as Yε{{tildeover (e)}₁,{tilde over (e)}₂}, {tilde over (e)}_(n) is a 2×1 columnselection vector with all zeros except for the n-th element with thevalue 1, {tilde over (e)}₁ represents a first column selected from thecodebook matrix V, and {tilde over (e)}₂ represents a second columnselected from the codebook matrix V.

The second element taken into account for a W₂ design is used to reflectinter-polarization phase information and can be designed similar to theDFT codebook in W₁ and with different quantization bits. The isco-phasing information can be shown as follows:

${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\; \frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

In summary, the second stage codebook set W₂ can be defined as followsaccording to different rank indication information:

For rank 1:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} \\{Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

Where (Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over(e)}₂, {tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂),({tilde over (e)}₂, {tilde over (e)}₁)}.

If column selection is the same for Y₁ and Y₂, then one bit is enough torepresent the column selection. The number of feedback bits for W₂ withrank 1 can be log₂ (N)+1 and log₂ (N)+2

For rank 2:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{3} \\{Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}} & {{- Y_{4}}^{j\frac{\; {2\pi \; n}}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

Where (Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j),{tilde over (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2).

With Y₃=Y₁ and Y₄=Y₂,

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{1} \\{Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}} & {{- Y_{2}}^{j\frac{\; {2\pi \; n}}{N}}}\end{bmatrix}} \right\}},{\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right);}$

and

With Y₃=Y₂ and Y₄=Y₁,

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}} & {{- Y_{1}}^{j\frac{\; {2\pi \; n}}{N}}}\end{bmatrix}} \right\}},{\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right).}$

Where (Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over(e)}₂, {tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂),({tilde over (e)}₂, {tilde over (e)}₁)}.

The rank-2 codebook has the same number of feedback bits log₂(N)+1 andlog₂(N)+2 as the rank-1 codebook for W2.

Advantageously a non-constant modulus property can be taken into accountto reflect inter-polarization amplitude information, and hereupon thethird element α reflecting the non-constant modulus property can beintroduced to W₂.

Then for rank 1,

${W_{2} \in \left\{ \begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}}\end{bmatrix} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

For rank 2,

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}} & {{- \alpha}\; Y_{4}^{j\frac{\; {2\pi \; n}}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

α is quantized in the range (0, 1):

In the event that the codebook matrix V in W₁ is formed of a set ofadjacent overlapped DFT vectors selected from the foregoing codebook c:

A column selection vector {tilde over (e)}_(n) is a 4×1 column selectionvector with all zeros except for the n-th element with the value 1,which indicates the selection of the n-th column vector from the matrixV, so there are four column vector possibilities in total, {{tilde over(e)}₁,{tilde over (e)}₂,{tilde over (e)}₃,{tilde over (e)}₄}. Y₁ and Y₂can be selected as any two of these four column vectors, so there are 16possibilities in total.

For rank 1:

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

Where (Y₁, Y₂)ε{({tilde over (e)}_(m), {tilde over (e)}_(k))}, (m=1, . .. 4, k=1, . . . , 4).

For rank 2,

${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{{j\frac{\; {2\pi \; n}}{N}}\;}} & {{- \alpha}\; Y_{4}^{j\frac{\; {2\pi \; n}}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$

Where

(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, (i=1, . . . 4, j=1, . . . , 4,k=1, . . . 4, l=1, . . . , 4).

The two-state codebook set W=W₁W₂ of the invention can be compatiblebackward with a Release 8 codebook. The two-state codebook set can beregarded as an improved design of the Release 8 codebook.

A method of determining a codebook from a two-state codebook set formedas above will be described below. The two-state codebook set is storedrespectively at the base station side and the user equipment side.

In an embodiment, referring to FIG. 1, firstly in the step S11, a basestation determines an uplink long-term and/or broadband channel matrixaccording to a sounding signal from a user equipment.

Then in the step S12, the base station selects a first codebook from afirst-stage codebook set W₁ based upon the first-stage codebook set W₁to match the uplink long-term and/or broadband channel matrix. Forexample, the base station can match the uplink long-term and/orbroadband channel matrix based upon a maximum capacity or minimumdistance criterion.

Next in the step S13, the base station sends index information of thedetermined first codebook to the user equipment.

Thus in the step S14, the user equipment selects the first codebook fromthe first-stage codebook set W₁ according to the index information ofthe first codebook from the base station upon reception of the indexinformation.

Then in the step S15, the user equipment determines a downlinkshort-term and/or narrowband channel matrix according to referenceinformation from the base station.

Next in the step S16, the user equipment selects a second codebook froma second-stage codebook set W₂ based upon the selected first codebook tomatch the downlink short-term and/or narrowband channel matrix. Forexample, the user equipment can multiply the first codebook with eachcodebook in the second-stage codebook set W₂ and select the secondcodebook from the second-stage codebook set W₂ based upon the is maximumcapacity or minimum distance criterion.

Thus in the step S17, the user equipment sends index information of thesecond codebook to the base station and multiplies the first codebookwith the second codebook to obtain a target codebook.

In the step S18, the base station selects the second codebook from thesecond-stage codebook set W₂ according to the index information of thesecond codebook from the user equipment upon reception of the indexinformation.

Then in the step S19, the base station multiplies the first codebookwith the second codebook to obtain the target codebook.

In another embodiment, referring to FIG. 2, firstly in the step S21, auser equipment determines a downlink long-term and/or broadband channelmatrix according to reference information from a base station.

Then in the step S22, the user equipment selects a first codebook from afirst-stage codebook set W₁ to match the downlink long-term and/orbroadband channel matrix. For example, the user equipment can match thedownlink long-term and/or broadband channel matrix based upon a maximumcapacity or minimum distance criterion.

Next in the step S23, the user equipment sends index information of thefirst codebook to the base station.

The base station selects the first codebook from the first-stagecodebook set W₁ according to the index information of the first codebookfrom the user equipment upon reception of the index information.

Then in the step S24, the user equipment determines a downlinkshort-term and/or narrowband channel matrix according to the referenceinformation from the base station.

Then in the step 25, the user equipment selects a second codebook from asecond-stage codebook set W₂ based upon the selected first codebook tomatch the downlink short-term and/or narrowband channel matrix. Forexample, the user equipment can multiply the first codebook with eachcodebook in the second second-stage codebook set W₂ and is select thesecond codebook from the second-stage codebook set W₂ based upon themaximum capacity or minimum distance criterion.

Next in the step S26, the user equipment sends index information of thesecond codebook to the base station and multiplies the first codebookwith the second codebook to obtain a target codebook.

The base station selects the second codebook from the second-stagecodebook set W₂ according to the index information of the secondcodebook from the user equipment upon reception of the indexinformation. Then the base station multiplies the first codebook withthe second codebook to obtain the target codebook.

Those skilled in the art shall appreciate that the invention apparentlywill not be limited to the foregoing exemplary embodiments and can beembodied in other specific forms without departing from the spirit oressence of the invention. Accordingly the embodiments shall be construedanyway to be exemplary and non-limiting. Any reference numerals in theclaims shall not be construed as limiting the scope of the invention.

Moreover apparently the term “comprising” will not preclude anotherelement(s) or step(s), and the term “a” or “an” will not precludeplural. A plurality of elements stated in an apparatus claim canalternatively be embodied as a single element. The terms “first”,“second”, etc., are intended to designate a name but not to suggest anyspecific order.

1. A method of generating a two-stage codebook set, the two-stagecodebook set being applicable to a multi-input multi-outputcommunication system in which a base station is configured with fourcross-polarized transmit antennas, and the two-stage codebook setincluding a first-stage codebook set and a second-stage codebook set,wherein the method comprises: generating a codebook matrix V based upona two-antenna rank-1 DFT codebook c; determining the first-stagecodebook set W₁ according to the codebook matrix V, wherein${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$ and determining the two-stage codebook set W₂ at leastbased upon a column selection vector and inter-polarization phaseinformation.
 2. The method according to claim 1, wherein the generatingcomprises: selecting two orthogonal DFT vectors from the two-antennarank-1 DFT codebook c to generate the codebook matrix V, wherein${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{\; {2\pi \; n}}{N}}\end{bmatrix}}^{T}},{\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)\mspace{14mu} {and}}$${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{\; {2\pi}}{N}m} & ^{j\frac{\; {2\pi}}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right).}$3. The method according to claim 1, wherein the generating comprises:selecting two orthogonal DFT vectors from the two-antenna rank-1 DFTcodebook c to generate a codebook matrix I, wherein${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{\; {2\pi \; n}}{N}}\end{bmatrix}}^{T}},{\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)\mspace{14mu} {and}}$${I = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{\; {2\pi}}{N}m} & ^{j\frac{\; {2\pi}}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right);}$and left-multiplying or right-multiplying the codebook matrix I by adiagonal matrix J to generate the codebook matrix V, wherein${J = \begin{pmatrix}\rho & 0 \\0 & \sqrt{1 - \rho^{2}}\end{pmatrix}},$ and ρ is quantized in the range (0, 1).
 4. The methodaccording to claim 1, wherein the generating comprises: selecting a setof adjacent overlapping DFT vectors from the two-antenna rank-1 DFTcodebook c to generate the codebook matrix V, wherein${V = \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\; \frac{2\pi}{N}m} & ^{j\; \frac{2\pi}{N}{({m + 1})}} & ^{j\; \frac{2\pi}{N}{({m + 2})}} & ^{j\; \frac{2\pi}{N}{({m + 3})}}\end{bmatrix}},{\left( {{m = 0},2,4,\ldots \mspace{14mu},{N - 2}} \right).}$5. The method according to claim 1, wherein the determining thetwo-stage codebook set W₂ comprises: determining the two-stage codebookset W₂ based upon the column selection vector and the inter-polarizationphase information in the formula of:${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} \\{Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{3} \\{Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- Y_{4}}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,wherein {tilde over (e)}_(z) represents a 2×1 selection vector in whichall other elements than an n-th element being 1 are 0, {tilde over (e)}₁represents a first column selected from the codebook matrix V, and{tilde over (e)}₂ represents a second column selected from the codebookmatrix V.
 6. The method according to claim 1, wherein the determiningthe two-stage codebook set W₂ comprises: determining the second set W₂based upon the column selection vector, the inter-polarization phaseinformation and inter-polarization amplitude information in the formulaof: ${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,wherein {tilde over (e)}_(n) represents a 2×1 selection vector in whichall other elements than an n-th element being 1 are 0, {tilde over (e)}₁represents a first column selected from the codebook matrix V, {tildeover (e)}₂ represents a second column selected from the codebook matrixV, and α is quantized in the range (0, 1).
 7. The method according toclaim 1, wherein the determining the two-stage codebook set W₂comprises: determining the second set W₂ based upon the column selectionvector, the inter-polarization phase information and inter-polarizationamplitude information in the formula of:${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}_(m), {tilde over (e)}_(k))}, (m=1, . . . 4,k=1, . . . , 4) for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, (i=1, . . . 4, j=1, . . . , 4,k=1, . . . 4, l=1, . . . , 4) for rank 2, wherein {tilde over (e)}_(n)represents a 4×1 selection vector in which all other elements than ann-th element being 1 are 0, {tilde over (e)}₁ represents a first columnselected from the codebook matrix V, {tilde over (e)}₂ represents asecond column selected from the codebook matrix V, {tilde over (e)}₃represents a third column selected from the codebook matrix V, {tildeover (e)}₄ represents a fourth column selected from the codebook matrixV, and α is quantized in the range (0, 1).
 8. A method of determining acodebook in a base station of a multi-input multi-output communicationsystem, the base station being configured with four cross-polarizedtransmit antennas, wherein the method comprises: determining an uplinklong-term and/or broadband channel matrix according to a sounding signalfrom a user equipment; selecting a first codebook from a first-stagecodebook set based upon the first-stage codebook set to match the uplinklong-term and/or broadband channel matrix; sending index information ofthe first codebook to the user equipment; receiving index information ofa second codebook from the user equipment; selecting the second codebookfrom a second-stage codebook set according to the index information ofthe second codebook; and multiplying the first codebook with the secondcodebook to obtain a target codebook, wherein the first-stage codebookset W₁ and the second-stage codebook set W₂ are determined by:generating a codebook matrix V based upon a two-antenna rank-1 DFTcodebook c; determining the first-stage codebook set W₁ according to thecodebook matrix V, wherein ${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$  and determining the second-stage codebook set W₂ atleast based upon a column selection vector and inter-polarization phaseinformation.
 9. The method according to claim 8, wherein the codebookmatrix V is generated by any one of: selecting two orthogonal DFTvectors from the two-antenna rank-1 DFT codebook c to generate thecodebook matrix V, wherein ${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},{\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)\mspace{14mu} {and}}$${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{{2\pi}\;}{N}m} & ^{j\frac{{2\pi}\;}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right);}$selecting two orthogonal DFT vectors from the two-antenna rank-1 DFTcodebook c to generate a codebook matrix I, wherein${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & ^{j\frac{2\pi \; n}{N}}\end{bmatrix}}^{T}},{\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)\mspace{14mu} {and}}$${I = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{{2\pi}\;}{N}m} & ^{j\frac{{2\pi}\;}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},\left( {{m = 0},1,{{\ldots \mspace{11mu} \frac{N}{2}} - 1}} \right),$and left-multiplying or right-multiplying the codebook matrix I by adiagonal matrix T to generate the codebook matrix V, wherein${J = \begin{pmatrix}\rho & 0 \\0 & \sqrt{1 - \rho^{2}}\end{pmatrix}},$ and ρ is quantized in the range (0, 1); and selecting aset of adjacent overlapping DFT vectors from the two-antenna rank-1 DFTcodebook c to generate the codebook matrix V, wherein${V = \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{{2\pi}\;}{N}m} & ^{j\frac{{2\pi}\;}{N}{({m + 1})}} & ^{j\frac{{2\pi}\;}{N}{({m + 2})}} & ^{j\frac{{2\pi}\;}{N}{({m + 3})}}\end{bmatrix}},{\left( {{m = 0},2,4,\ldots \mspace{14mu},{N - 2}} \right).}$10. The method according to claim 8, wherein the second-stage codebookset W₂ is determined by any one of: determining the second set W₂ basedupon the column selection vector and the inter-polarization phaseinformation in the formula of:${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,wherein {tilde over (e)}_(n) represents a 2×1 selection vector in whichall other elements than an n-th element being 1 are 0, {tilde over (e)}₁represents a first column selected from the codebook matrix V, and{tilde over (e)}₂ represents a second column selected from the codebookmatrix V; determining the second set W₂ based upon the column selectionvector, the inter-polarization phase information and inter-polarizationamplitude information in the formula of:${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,wherein {tilde over (e)}_(n) represents a 2×1 selection vector in whichall other elements than an n-th element being 1 are 0, {tilde over (e)}₁represents a first column selected from the codebook matrix V, {tildeover (e)}₂ represents a second column selected from the codebook matrixV, and α is quantized in the range (0, 1); and determining the secondset W₂ based upon the column selection vector, the inter-polarizationphase information and inter-polarization amplitude information in theformula of: ${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}_(m), {tilde over (e)}_(k))}, (m=1, . . . 4,k=1, . . . , 4) for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, (i=1, . . . 4, j=1, . . . , 4,k=1, . . . 4, l=1, . . . , 4) for rank 2, wherein {tilde over (e)}_(n)represents a 4×1 selection vector in which all other elements than ann-th element being 1 are 0, {tilde over (e)}₁ represents a first columnselected from the codebook matrix V, {tilde over (e)}₂ represents asecond column selected from the codebook matrix V, represents a thirdcolumn selected from the codebook matrix V, {tilde over (e)}₄ representsa fourth column selected from the codebook matrix V, and α is quantizedin the range (0, 1).
 11. A method of determining a codebook in a userequipment of a multi-input multi-output communication system, whereinthe method comprises: receiving index information of a first codebookfrom a base station; selecting the first codebook from a first-stagecodebook set according to the index information of the first codebook;determining a downlink short-term and/or narrowband channel matrixaccording to reference information from the base station; selecting asecond codebook from a second-stage codebook set based upon the firstcodebook to match the downlink short-term and/or narrowband channelmatrix; and sending index information of the second codebook to the basestation and multiplying the first codebook with the second codebook toobtain a target codebook, wherein the first-stage codebook set W₁ andthe second-stage codebook set W₂ are determined by: generating acodebook matrix V based upon a two-antenna rank-1 DFT codebook c;determining the first-stage codebook set W₁ according to the codebookmatrix V, wherein ${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$  and determining the second-stage codebook set W₂ atleast based upon a column selection vector and inter-polarization phaseinformation.
 12. The method according to claim 11, wherein the selectingcomprises: multiplying the first codebook with each codebook in thesecond-stage codebook set and selecting the second codebook from thesecond-stage codebook set based upon a maximum capacity or minimumdistance criterion.
 13. A method of determining a codebook in a userequipment of a multi-input multi-output communication system, whereinthe method comprises: determining a downlink long-term and/or broadbandchannel matrix according to reference information from a base station;selecting a first codebook from a first-stage codebook set to match thedownlink long-term and/or broadband channel matrix; sending indexinformation of the first codebook to the base station; determining adownlink short-term and/or narrowband channel matrix according to thereference information from the base station; selecting a second codebookfrom a second-stage codebook set based upon the first codebook to matchthe downlink short-term and/or narrowband channel matrix; and sendingindex information of the second codebook to the base station, andmultiplying the first codebook with the second codebook to obtain atarget codebook, wherein the first-stage codebook set W₁ and thesecond-stage codebook set W₂ are determined by: generating a codebookmatrix V based upon a two-antenna rank-1 DFT codebook c; determining thefirst-stage codebook set W₁ according to the codebook matrix V, wherein${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$  and determining the second-stage codebook set W₂ atleast based upon a column selection vector and inter-polarization phaseinformation.
 14. The method according to claim 13, wherein the codebookmatrix V is generated by any one of: selecting two orthogonal DFTvectors from the two-antenna rank-1 DFT codebook c to generate thecodebook matrix V, wherein ${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {^{j\frac{2\pi \; n}{N}}\;}\end{bmatrix}}^{T}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$and ${V = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},{\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right);}$selecting two orthogonal DFT vectors from the two-antenna rank-1 DFTcodebook c to generate a codebook matrix I, wherein${c = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {^{j\frac{2\pi \; n}{N}}\;}\end{bmatrix}}^{T}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right)$and ${I = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + \frac{N}{2}})}}\end{bmatrix}}},\left( {{m = 0},1,\ldots \mspace{14mu},{\frac{N}{2} - 1}} \right),$and left-multiplying or right-multiplying the codebook matrix I by adiagonal matrix J to generate the codebook matrix V, wherein${J = \begin{pmatrix}\rho & 0 \\0 & \sqrt{1 - \rho^{2}}\end{pmatrix}},$ and ρ is quantized in the range (0, 1); and selecting aset of adjacent overlapping DFT vectors from the two-antenna rank-1 DFTcodebook c to generate the codebook matrix V, wherein${V = \begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{N}m} & ^{j\frac{2\pi}{N}{({m + 1})}} & ^{j\frac{2\pi}{N}{({m + 2})}} & ^{j\frac{2\pi}{N}{({m + 3})}}\end{bmatrix}},{\left( {{m = 0},2,4,\ldots \mspace{14mu},{N - 2}} \right).}$15. The method according to claim 13, wherein the second-stage codebookset W₂ is determined by any one of: determining the second set W₂ basedupon the column selection vector and the inter-polarization phaseinformation in the formula of:${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,wherein {tilde over (e)}_(n) represents a 2×1 selection vector in whichall other elements than an n-th element being 1 are 0, {tilde over (e)}₁represents a first column selected from the codebook matrix V, and{tilde over (e)}₂ represents a second column selected from the codebookmatrix V; determining the second set W₂ based upon the column selectionvector, the inter-polarization phase information and inter-polarizationamplitude information in the formula of:${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}₁, {tilde over (e)}₁), ({tilde over (e)}₂,{tilde over (e)}₂), ({tilde over (e)}₁, {tilde over (e)}₂), ({tilde over(e)}₂, {tilde over (e)}₁)} for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, i, j, k, lε(1,2) for rank 2,wherein {tilde over (e)}_(n) represents a 2×1 selection vector in whichall other elements than an n-th element being 1 are 0, {tilde over (e)}₁represents a first column selected from the codebook matrix V, {tildeover (e)}₂ represents a second column selected from the codebook matrixV, and α is quantized in the range (0, 1); and determining the secondset W₂ based upon the column selection vector, the inter-polarizationphase information and inter-polarization amplitude information in theformula of: ${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂)ε{({tilde over (e)}_(m), {tilde over (e)}_(k))}, (m=1, . . . 4,k=1, . . . , 4) for rank 1; and${W_{2} \in \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}{\alpha \; Y_{1}} & {\sqrt{1 - \alpha^{2}}Y_{3}} \\{\sqrt{1 - \alpha^{2}}Y_{2}^{j\frac{2\pi \; n}{N}}} & {{- \alpha}\; Y_{4}^{j\frac{2\pi \; n}{N}}}\end{bmatrix}} \right\}},\left( {{n = 0},1,\ldots \mspace{14mu},{N - 1}} \right),$(Y₁, Y₂, Y₃, Y₄)ε{({tilde over (e)}_(i), {tilde over (e)}_(j), {tildeover (e)}_(k), {tilde over (e)}_(l))}, (i=1, . . . 4, j=1, . . . , 4,k=1, . . . 4, l=1, . . . , 4) for rank 2, wherein {tilde over (e)}_(n)represents a 4×1 selection vector in which all other elements than ann-th element being 1 are 0, {tilde over (e)}₁ represents a first columnselected from the codebook matrix V, {tilde over (e)}₂ represents asecond column selected from the codebook matrix V, {tilde over (e)}₃represents a third column selected from the codebook matrix V, {tildeover (e)}₄ represents a fourth column selected from the codebook matrixV, and α is quantized in the range (0, 1).
 16. The method according toclaim 13, wherein the selecting comprises: multiplying the firstcodebook with each codebook in the second-stage codebook set andselecting the second codebook from the second-stage codebook set basedupon a maximum capacity or minimum distance criterion.
 17. A method ofdetermining a codebook in a base station of a multi-input multi-outputcommunication system, the base station being configured with fourcross-polarized transmit antennas, wherein the method comprises thesteps of: receiving index information of a first codebook from a userequipment; selecting the first codebook from a first-stage codebook setaccording to the index information of the first codebook; receivingindex information of a second codebook from the user equipment;selecting the second codebook from a second-stage codebook set accordingto the index information of the second codebook; and multiplying thefirst codebook with the second codebook to obtain a target codebook,wherein the first-stage codebook set W₁ and the second-stage codebookset W₂ are determined by: generating a codebook matrix V based upon atwo-antenna rank-1 DFT codebook c; determining the first-stage codebookset W₁ according to the codebook matrix V, wherein${W_{1} = \begin{bmatrix}V & 0 \\0 & V\end{bmatrix}};$ and determining the second-stage codebook set W₂ atleast based upon a column selection vector and inter-polarization phaseinformation.